1. Field of the Invention
This invention relates generally to communication systems wherein modulated carrier signals convey data in digital form and more particularly to the implementation of coherent demodulators and signal phase estimators for such systems which must accommodate undesired signal-phase values and temporal variations thereof.
2. Description of the Related Art
In many carrier-based communication systems the transmit signals used to convey information are of the form EQU s.sub.tx (t.sub.tx)=A.sub.tx (t.sub.tx).multidot.sin [.omega..sub.ctx .multidot.t.sub.tx +.phi..sub.mtx (t.sub.tx)] (1)
where t.sub.tx represents (relative) transmit time, .omega..sub.ctx represents the transmit radian carrier frequency in radians per second, .phi..sub.mtx (t.sub.tx) represents signal phase variations attributable to any phase modulation effected and A.sub.tx (t.sub.tx) represents the signal's amplitude. When the information transmitted is digital in form, the time continuum is generally divided into a succession of contiguous signaling (modulation) intervals and, for each signaling interval, log .sub.2 m (uncoded or coded) data bits select one of m pre-specified options for varying the signal's phase and/or amplitude during the signaling interval. For this invention, the signal's phase may be varied (modulated) to convey digital data using any one of many different modulation schemes including m-ary phase shift keying (PSK), m-ary continuous-phase frequency shift keying (CPFSK) and m-ary CPFSK with modulation and convolutional data encoding effected jointly. The signal's amplitude may vary with time as a consequence of implementing an amplitude modulation scheme such as m-ary amplitude shift keying (ASK) or incidentally, e.g., due to signal filtering effected. For m-ary ASK, modulation phase component .phi..sub.mtx (t.sub.tx) has a constant value considered herein to be zero radian. This invention also applies to several modulation schemes for which signal amplitude and signal phase are varied jointly to convey digital data as for m-ary quadrature amplitude modulation (QAM).
For each of several modulation schemes, the transmitted signal can be modeled equivalently as either a phase modulated signal or an amplitude modulated signal where the signal amplitude is represented by either a real or complex-valued function of time. Such schemes are considered to effect phase modulation herein irrespective of the means used to generate the signals transmitted. Further, for communication systems wherein digital data are transmitted via signaling bursts rather than continuously--as in time division multiple access (TDMA) systems--a transmit signal is modeled by assigning a value of zero to the signal's amplitude whenever signal transmission is disabled.
A transmit signal propagates from its point of origin to one or more receiver locations via one or more communication channels comprised of wire-line, wireless or electronic relay means, or any combination thereof. For a transmit signal representable by Equation 1, a signal received at a receiver location is of the form EQU s.sub.rx (t)=s(t)+n.sub..SIGMA. (t) (2)
where t represents (relative) receive time, s(t) is a delayed, attenuated and generally distorted version of the transmit signal, EQU s(t)=A(t).multidot.sin [.omega..sub.c .multidot.t+.phi..sub.m (t)+.phi..sub.u (t)], (3)
and n.sub..SIGMA. (t) represents a sum of noise and undesired signals which exacerbate generation of an exact (delayed) replica of the transmit data at the receiver. In accord with common practice, radian carrier frequency .omega..sub.c is assumed to be perfectly known at the receiver; frequency uncertainties that result from imperfect frequency synthesis within transmit, relay and receive subsystems and any doppler shift experienced by the signal in propagating to the receiver are considered to affect the value of signal phase .phi..sub.u (t): a phase variation that is unintended and undesired. Signal parameter .phi..sub.m (t) represents the modulation component of the received signal's phase when phase modulation is effected; otherwise, its value is considered herein to equal zero radian.
For a communication system wherein undesired signal-phase .phi..sub.u (t) can be made to vary slowly relative to and be distinguishable from phase .phi..sub.m (t), the most effective use of signal power can generally be achieved by employing a coherent demodulator to process the received signal. Ideally, a portion of the receiver would generate an exact replica of signal phase .phi..sub.u (t) and subtract this replica from the phase of the received signal to form a signal which exhibits no undesired phase variations; the latter signal would then be demodulated coherently to generate a nominal replica of the transmitted data stream. For many classes of modulation schemes, prior art provides means for coherently demodulating signals which exhibit no undesired phase variations that can be implemented effectively whenever time intervals spanned by received modulation symbols, modulation intervals, can be accurately determined at the receiver's location.
In practice, undesired signal-phase .phi..sub.u (t) cannot be replicated exactly at a receiver location, but an estimate of .phi..sub.m (t) can often be generated with sufficient accuracy to allow the implementation of nearly-ideal coherent demodulation--particularly when m-ary PSK is used to generate signal modulation phase .phi..sub.m (t). For ideal (unfiltered) m-ary PSK, the signal's amplitude has a constant value and .phi..sub.u (t) assumes any one of m phases that are equally spaced in a 2 .pi. radians phase range during each modulation interval. As is well known, an m.sup.th -order nonlinear device having a received m-ary PSK signal applied to its input port and a bandpass filter that rejects undesired components in the nonlinear device's output signal can generate a signal having a radian center frequency of m.multidot..omega..sub.c and phase m.multidot..phi..sub.u (t) accompanied by a noise signal that derives from the n.sub..SIGMA. (t) component of the received signal. That is, an m.sup.th -order nonlinear device provides a means for distinguishing m.multidot..phi..sub.u (t) from .phi..sub.m (t) when m-ary PSK is implemented. The nonlinear device's output signal is typically filtered by a relatively narrow-band phase-lock loop to generate a sufficiently accurate estimate of phase m.multidot..phi..sub.u (t), notwithstanding the presence of noise in the received signal. An ambiguous estimate of phase .phi..sub.u (t) can be determined therefrom by effectively dividing m.multidot..phi..sub.u (t) by m. An m-fold ambiguity that derives from the divide operation is generally accommodated by either 1) differentially encoding the transmit data stream and differentially decoding the demodulated data stream in a manner appropriated for the value of m implemented or 2) periodically embedding a priori specified symbols within the transmit date stream which replicate properly in the demodulator only when the appropriate one of m ambiguous phase values is selected. Alternatively, phase-lock loops that incorporate other forms of nonlinearities to distinguish .phi..sub.u (t) from .phi..sub.m (t), e.g., a Costas loop, can be used to provide the desired phase estimate when m-ary PSK modulation is employed.
Phase-lock loops which incorporate nonlinearities as described in the preceding paragraph have attributes which limit system performances--particularly when burst signals are used to convey data as in TDMA systems. As is well known, the time required for a phase-lock loop to achieve lock is statistically distributed and occasionally exceeds the mean acquisition time by a considerable amount (such an event is referred to as a phase-lock loop hang-up), and the noise component of the received signal occasionally causes a locked loop to cycle slip, i.e., to lose and regain lock in a manner whereby the accumulated phase of the loop's output signal differs from the accumulated phase of the (multiplied) signal being tracked by one or more cycles. Further, as the nonlinearity order--the value of m--is increased, the power spectral density of the noise signal at the output of the nonlinearity increases relative to the level of the desired output signal because a larger number of signal by noise products are generated. Correspondingly, the bandwidth of the signal phase tracking loop must be made increasingly narrow relative to the modulation symbol transmission rate to achieve acceptable steady-state performance. Filtering an m-ary PSK transmit signal to reduce spectral sidelobe levels can also cause tracking-loop performance to degrade.
For a TDMA system wherein estimates of carrier frequency, carrier phase and modulation interval timing are generated at the beginning of each received signal burst by processing preamble symbols (before data demodulation is initiated), making the bandwidths of tracking loops sufficiently small to achieve acceptable steady-state performance can necessitate the use of an unacceptably long burst preamble. For a symbol-synchronous TDMA system, i.e., for a TDMA system wherein signal modulation symbol time bases and carrier frequencies are maintained in accurate synchronism with the time base and frequency, respectively, of a (pulsed-envelope) network timing signal, the transmission of burst preambles can be avoided by converting the received signal bursts into digitally represented sample sequences that are stored in digital memory and implementing "multiple-pass" digital processing. Typically, in-phase and quadrature components of the received signal are integrated over each modulation interval and converted into digital form or, equivalently, appropriate digitized signal sample values are summed to generate the sample sequences processed. Paired in-phase and quadrature sample values are interpreted as vectors from which vectors which have phase angles equal to m times the sample vector angles are generated and processed digitally over a sliding processing window to form estimated values of m.multidot..phi..sub.u (t) modulo 2 .pi. radians. These values are divided by m to generate estimated values of .phi..sub.u (t) which exhibit an m-fold ambiguity. In turn, stored (delayed) sample vectors are rotated in phase as appropriate to correct for the estimated undesired signal-phase values and the phase-corrected sample vectors are demodulated to generate a received data sequence. Of course, such multiple-pass digital processing does not circumvent the fundamental limitations of m.sup.th -order nonlinear phase estimation methods.
Estimation of an undesired signal-phase component can similarly be accomplished when certain combinations of phase and amplitude modulations are used to convey data, e.g., as for selected forms of QAM. However, important modulation methods are incompatible with the use of nonlinear processing to distinguish undesired signal-phase variation .phi..sub.u (t) from signal phase modulation .phi..sub.m (t)--including most forms of m-ary CPFSK. Circumvention of m.sup.th -order nonlinear processor performance limitations is also of interest.
One alternative approach to distinguishing .phi..sub.u (t) from .phi..sub.m (t) relies on estimation of .phi..sub.m (t) and, effectively, subtraction of the estimated modulation phase from the phase of the received signal to generate a signal which, ideally, would exhibit phase variations .phi..sub.u (t) only. Estimators which incorporate this alternative approach are often referred to as either decision-directed estimators or data-aided estimators. Their utility derives from the premise that sufficiently accurate estimation of .phi..sub.u (t) can be accomplished using an estimate of .phi..sub.m (t) that is not sufficiently accurate for demodulation purposes--at least whenever the error in the locally generated estimate of .phi..sub.u (t) is large. Proper operation of a decision-directed estimator requires that the modulation means and estimator be implemented jointly in a manner whereby errors made in estimating .phi..sub.m (t) only temporarily affect estimator operation and contribute only incrementally to errors made in estimating .phi..sub.u (t) and demodulating the received signal. This requirement substantially limits the scope of applications for which decision-directed (and data-aided) estimators can be implemented effectively.